fmri-mahalanobis-bures-whitening

name	fmri-mahalanobis-bures-whitening
description	De-individualizing fMRI signals via Mahalanobis whitening and Bures geometry — methodology for distilling meaningful information from fMRI by treating data whitening as quantum-inspired state de-individualization using Bures distance.
activation_keywords	["fMRI de-individualization","Mahalanobis whitening brain","Bures distance fMRI","fMRI functional connectivity","quantum-inspired brain analysis","功能连接去个体化","fMRI白化","Bures几何脑成像","Alzheimer fMRI biomarker","functional connectivity preprocessing"]
categories	["neuroscience","medical-imaging","quantum-physics"]
arxiv_id	2511.07313
arxiv_url	https://arxiv.org/abs/2511.07313
authors	Aaron Jacobson, Tingting Dan, Martin Styner, Guorong Wu, Shahar Kovalsky, Caroline Moosmueller
created	2026-06-08

De-Individualizing fMRI Signals via Mahalanobis Whitening and Bures Geometry

Description

Methodology for processing fMRI signals through Mahalanobis data whitening to extract meaningful information about subjects and experimental stimuli. Provides a quantum-inspired interpretation of whitening as a two-stage de-individualization process motivated by the Bures distance from quantum mechanics. Applications include improving Alzheimer's diagnosis accuracy, especially in preclinical stages.

Core Concepts

Mahalanobis Whitening for fMRI

• Standard fMRI analysis suffers from subject-specific confounds
• Mahalanobis whitening: x_whitened = Σ^(-1/2) · (x - μ)
• Removes individual covariance structure while preserving stimulus-relevant information
• Two-stage process: (1) remove subject identity, (2) preserve experimental signal

Bures Distance Connection

• Bures distance: D_B(ρ₁, ρ₂) = √[2(1 - Tr√(√ρ₁·ρ₂·√ρ₁))]
• Quantum metric for distinguishing quantum states
• Applied to fMRI covariance matrices as "quantum states" of brain activity
• Provides geometrically meaningful distance between brain states

Methodology Steps

Step 1: Compute Subject Covariance

For each subject s:
  Σ_s = Cov(fMRI_time_series_s)
  μ_s = Mean(fMRI_time_series_s)

Step 2: Apply Mahalanobis Whitening

Global covariance: Σ_global = Average(Σ_s) across subjects
Whitening matrix: W = Σ_global^(-1/2)
Whitened data: x' = W · (x - μ_global)

Step 3: Bures Distance Analysis

Treat each subject's covariance as density matrix: ρ_s = Σ_s / Tr(Σ_s)
Compute Bures distance between subject states:
  D_B(ρ_s, ρ_t) = √[2(1 - Tr√(√ρ_s · ρ_t · √ρ_s))]

Step 4: De-Individualization Validation

• Verify that whitened data no longer encodes subject identity
• Confirm that stimulus/experimental effects are preserved
• Use cross-validation on downstream tasks (classification, prediction)

Applications

1. Alzheimer's diagnosis: Improved accuracy in preclinical stage detection
2. Cross-subject fMRI analysis: Remove individual confounds for group studies
3. Biomarker discovery: Isolate disease-relevant signals from individual variation
4. Brain-computer interfaces: Standardized features across subjects
5. Longitudinal studies: Track changes within subjects over time

Key Advantages